Dynamics of Moving bodies

``A problem with defining force as rate of change of linear momentum'': Let us consider a body of mass m, moving with velocity u initially, in the next time interval it is acted by a force in the direction of motion, and at instant t$+$ its mass is M and velocity v. F$\cdot $t$=$Mv-mu or,v$=$ m/M.u$+$F/M.t or,v$=$B.u$+$A.t where A$=$F/M,B$=$m/M. So other eqn of motion are: dS$=$vdt or dS$=$(B.u$+$A.t)dt or S$=$B.u.t$+$A/2.t\textasciicircum 2 Andv\textasciicircum 2$=$B\textasciicircum 2 u\textasciicircum 2$+$2A$\cdot $B$\cdot $u$\cdot $t$+$A\textasciicircum 2 t\textasciicircum 2 or,v\textasciicircum 2$=$B\textasciicircum 2 u\textasciicircum 2$+$2A.S However, defining acceleration as rate of change of velocity, we have established an identity v$=$u$+$a.t which is independent of choice of v, u. M\textgreater \textgreater m, B is very small, product B.u or its higher power always tend to be negligible, even in cases when u is finitely large.In cases v$\to $c,F,M$\to \infty $, thus A becomes indeterminate.There is inconvenience as A, B are not predetermined and are functions of u, v and thus the definition goes in circle. Hence we conclude, our hypothesis that force$=$rate of change of linear momentum is not sufficient; we would now find trial solutions to define force in most convenient way.